The DO Loop

Analytics | Learn SAS | Programming Tips

Rick WicklinApril 17, 2023 3

Should you use the Wald confidence interval for a binomial proportion?

The "Teacher’s Corner" of The American Statistician enables statisticians to discuss topics that are relevant to teaching and learning statistics. Sometimes, the articles have practical relevance, too. Andersson (2023) "The Wald Confidence Interval for a Binomial p as an Illuminating 'Bad' Example," is intended for professors and masters-level students in

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Analytics

Rick WicklinApril 10, 2023 6

Means and medians of subgroups

A journal article listed the mean, median, and size for subgroups of the data, but did not report the overall mean or median. A SAS programmer wondered what, if any, inferences could be made about the overall mean and median for the data. The answer is that you can calculate

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Analytics

Rick WicklinFebruary 22, 2023 3

What is the metalog distribution?

The metalog family of distributions (Keelin, Decision Analysis, 2016) is a flexible family that can model a wide range of continuous univariate data distributions when the data-generating mechanism is unknown. This article provides an overview of the metalog distributions. A subsequent article shows how to download and use a library

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Analytics

Rick WicklinSeptember 28, 2022 1

Definitions of moments in probability and statistics

The moments of a continuous probability distribution are often used to describe the shape of the probability density function (PDF). The first four moments (if they exist) are well known because they correspond to familiar descriptive statistics: The first raw moment is the mean of a distribution. For a random

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Analytics | Programming Tips

Rick WicklinMay 25, 2022 0

How much does a bootstrap estimate depend on the random number stream?

Many modern statistical techniques incorporate randomness: simulation, bootstrapping, random forests, and so forth. To use the technique, you need to specify a seed value, which determines pseudorandom numbers that are used in the algorithm. Consequently, the seed value also determines the results of the algorithm. In theory, if you know

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Programming Tips

Rick WicklinJanuary 20, 2022 6

How often do different statistical tests agree? A simulation study

Here's a fun problem to think about: Suppose that you have two different valid ways to test a statistical hypothesis. For a given sample, will both tests reject or fail to reject the hypothesis? Or might one test reject it whereas the other does not? The answer is that two

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Analytics | Data Visualization

Rick WicklinNovember 8, 2021 0

The normal approximation and random samples of the binomial distribution

Recall that the binomial distribution is the distribution of the number of successes in a set of independent Bernoulli trials, each having the same probability of success. Most introductory statistics textbooks discuss the approximation of the binomial distribution by the normal distribution. The graph to the right shows that the

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Analytics | Learn SAS

Rick WicklinOctober 4, 2021 2

Choose samples with specified statistical properties

A reader asked whether it is possible to find a bootstrap sample that has some desirable properties. I am using the term "bootstrap sample" to refer to the result of randomly resampling with replacement from a data set. Specifically, he wanted to find a bootstrap sample that has a specific

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Analytics

Rick WicklinAugust 16, 2021 3

Rankings and the geometry of weighted averages

People love rankings. You've probably seen articles about the best places to live, the best colleges to attend, the best pizza to order, and so on. Each of these is an example of a ranking that is based on multiple characteristics. For example, a list of the best places to

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Programming Tips

Rick WicklinJune 23, 2021 2

The probability integral transform

This article uses simulation to demonstrate the fact that any continuous distribution can be transformed into the uniform distribution on (0,1). The function that performs this transformation is a familiar one: it is the cumulative distribution function (CDF). A continuous CDF is defined as an integral, so the transformation is

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